Publications by Ulugbek Kamilov

Inference for Generalized Linear Models via Alternating Directions and Bethe Free Energy Minimization

Generalized linear models, where a random vector x is observed through a noisy, possibly nonlinear, function of a linear transform z = A x, arise in a range of applications in nonlinear filtering and regression. Approximate message passing (AMP) methods, b ...

IEEE2017

Optical Tomography Based On A Nonlinear Model That Handles Multiple Scattering

Michaël Unser, Demetri Psaltis, Ulugbek Kamilov, Alexandre Goy, Joowon Lim

Learning Tomography (LT) is a nonlinear optimization algorithm for computationally imaging three-dimensional (3D) distribution of the refractive index in semi-transparent samples. Since the energy function in LT is generally non-convex, the solution it obt ...

Ieee2017

Optical Tomographic Image Reconstruction Based on Beam Propagation and Sparse Regularization

Michaël Unser, Cédric René Jean Vonesch, Demetri Psaltis, Ulugbek Kamilov

Optical tomographic imaging requires an accurate forward model as well as regularization to mitigate missing-data artifacts and to suppress noise. Nonlinear forward models can provide more accurate interpretation of the measured data than their linear coun ...

2016

Learning from Examples in Optical Imaging

Michaël Unser, Cédric René Jean Vonesch, Demetri Psaltis, Ulugbek Kamilov

Imaging systems can be designed using examples and methods similar to the techniques used in deep learning. We describe experimental results demonstrating optical tomography based on the learning approach. ...

OSA2016

Inference for Generalized Linear Models via Alternating Directions and Bethe Free Energy Minimization

Ulugbek Kamilov

Generalized Linear Models (GLMs), where a random vector x is observed through a noisy, possibly nonlinear, function of a linear transform z = A x arise in a range of applications in nonlinear filtering and regression. Approximate Message Passing (AMP) meth ...

IEEE2015

Learning Approach to Optical Tomography

Michaël Unser, Cédric René Jean Vonesch, Demetri Psaltis, Ulugbek Kamilov, Alexandre Goy

Optical tomography has been widely investigated for biomedical imaging applications. In recent years optical tomography has been combined with digital holography and has been employed to produce high-quality images of phase objects such as cells. In this p ...

Optical Soc Amer2015

Isotropic Inverse-Problem Approach for Two-Dimensional Phase Unwrapping

Michaël Unser, Demetri Psaltis, Ulugbek Kamilov

We propose a new technique for two-dimensional phase unwrapping. The unwrapped phase is found as the solution of an inverse problem that consists in the minimization of an energy functional. The latter includes a weighted data fidelity term that favors spa ...

JOSA2015

Sparsity-Driven Statistical Inference for Inverse Problems

Ulugbek Kamilov

This thesis addresses statistical inference for the resolution of inverse problems. Our work is motivated by the recent trend whereby classical linear methods are being replaced by nonlinear alternatives that rely on the sparsity of naturally occurring sig ...

EPFL2015

Approximate Message Passing With Consistent Parameter Estimation and Applications to Sparse Learning

Michaël Unser, Ulugbek Kamilov

We consider the estimation of an independent and identically distributed (i.i.d.) (possibly non-Gaussian) vector x is an element of R-n from measurements y is an element of R-m obtained by a general cascade model consisting of a known linear transform foll ...

Ieee-Inst Electrical Electronics Engineers Inc2014

Variational Justification of Cycle Spinning for Wavelet-Based Solutions of Inverse Problems

Michaël Unser, Emrah Bostan, Ulugbek Kamilov

Cycle spinning is a widely used approach for improving the performance of wavelet-based methods that solve linear inverse problems. Extensive numerical experiments have shown that it significantly improves the quality of the recovered signal without increa ...

IEEE Institute of Electrical and Electronics Engineers2014